Simplify the following expression and state the condition under which the simplification is valid. $y = \dfrac{-9n^2 - 18n + 720}{n^3 - 18n^2 + 80n}$
Explanation: First factor out the greatest common factors in the numerator and in the denominator. $ y = \dfrac {-9(n^2 + 2n - 80)} {n(n^2 - 18n + 80)} $ $ y = -\dfrac{9}{n} \cdot \dfrac{n^2 + 2n - 80}{n^2 - 18n + 80} $ Next factor the numerator and denominator. $ y = - \dfrac{9}{n} \cdot \dfrac{(n - 8)(n + 10)}{(n - 8)(n - 10)}$ Assuming $n \neq 8$ , we can cancel the $n - 8$ $ y = - \dfrac{9}{n} \cdot \dfrac{n + 10}{n - 10}$ Therefore: $ y = \dfrac{ -9(n + 10)}{ n(n - 10)}$, $n \neq 8$